Structural Properties of β-Dodecylmaltoside and C12E6 Mixed Micelles

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Structural Properties of β-Dodecylmaltoside and C12E6 Mixed Micelles )

:: :: Petra Baverback,† Cristiano L. P. Oliveira,† Vasil M. Garamus,‡ Imre Varga,§ Per M. Claesson,§, and Jan Skov Pedersen*,† †

)

Department of Chemistry and iNANO Interdisciplinary Nanoscience Center, University of Aarhus, Langelandsgade 140, DK-8000 A˚rhus C, Denmark, ‡GKSS Research Centre, Max Planck Strasse, D-21502 Geesthacht, Germany , §Royal Institute of Technology, Department of Chemistry, Surface Chemistry, Drottning :: Kristinas vag 51, SE-100 44 Stockholm, Sweden, and Institute for Surface Chemistry, Box 5607, SE-114 86 Stockholm, Sweden Received January 27, 2009. Revised Manuscript Received February 27, 2009 Mixed micelles formed in aqueous solutions of nonionic surfactants n-dodecyl-hexaethylene-glycol (C12E6) and n-dodecyl-β-D-maltoside (C12G2) have been studied using small-angle neutron and X-ray scattering (SANS and SAXS) and static light scattering (SLS). Apparent micelle molar masses obtained with SLS were analyzed with a model taking into account both micelle growth and interference effects. The analysis shows that pure C12G2 forms small globular micelles whereas C12E6 and the mixtures form elongated micelles of much higher molar mass. The elongated micelles grow with increased concentration according to mean-field theory, and the masses are larger for increasing amounts of C12E6. To describe the SANS and SAXS data for C12E6 and the mixtures, it was necessary to employ a model with coexisting spherical and spherocylindrical micelles. The SANS and SAXS data were fitted simultaneously using this model with core-shell particles and molecular constraints. All mixtures, as well as pure C12E6, can be described by this model, demonstrating the coexistence of spherical and cylindrical micelles. The spherical micelles are the same size in all samples, whereas the cylindrical micelles grow in length with the fraction of C12E6 in the samples, as well as with concentration, in agreement with the SLS analysis. The mass fraction of surfactant in cylindrical aggregates also increases with the fraction of C12E6 and with overall concentration. The analysis of the SAXS and SANS data for pure C12G2 shows that the micelles are disk-shaped. The presence of elongated micelles in pure C12E6 and in the mixtures demonstrates that the behavior of the mixtures is dominated by C12E6.

Introduction Above the critical micelle concentration (cmc), surfactants in aqueous solution spontaneously aggregate into micelles in which the hydrophobic tails are separated from surrounding water by a layer of polar headgroups. Self-assembled aggregates exist in different shapes such as spheres and cylinders as well as larger structures such as lamellae and giant polymerlike micelles. Which type is formed depends on factors such as the structure of the surfactant head and tail groups, surfactant and/or electrolyte concentration, addition of cosurfactant, and temperature and may therefore change with any of these parameters.1 Micelle shape and size are important to the characteristics of the system because they determine the rheology of the surfactant solution. In most applications, more than one surfactant is used because synergistic effects can improve the performance. As an example, nonionic surfactants are often added to ionic ones to decrease the repulsion between headgroups, thus facilitating micellization and improving the solubilizing capability of the system.1 Even stronger effects are obtained if the hydrophilic groups are oppositely :: charged. This is reflected in the studies of Bergstrom and 2,3 Pedersen, who showed that catanionic surfactant mixtures display a wide range of micelle geometries upon changing the composition, and therefore the surface charge density, of the aggregates. In this work, we have studied the micelles formed by mixtures of two nonionic surfactants, namely, n-dodecyl-β-D-maltoside *Corresponding author. E-mail: [email protected].

:: (1) Holmberg, K.; Jonsson, B.; Kronberg, B.; Lindman, B. Surfactants and Polymers in Aqueous Solution, 2nd ed.; John Wiley & Sons: New York, 2003. (2) Bergstrom, M.; Pedersen, J. S. J. Phys. Chem. B 1999, 103, 8502. (3) Bergstrom, M.; Pedersen, J. S.; Schurtenberger, P.; Egelhaaf, S. U. J. Phys. Chem. B 1999, 103, 9888.

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(C12G2) and n-dodecyl-hexaethylene-glycol (C12E6). C12G2 belongs to the glucoside-based surfactants, which can be made from renewable materials and are biodegradable4 and therefore very interesting from an environmental point of view. Often these molecules are used together with other well-known, more traditional nonionic surfactants such as the ethylene oxidebased ones to achieve optimal performance. Features of the self-aggregation of ionic or nonionic CiEj surfactants are difficult or impossible to apply to alkyl glycosides in a direct and meaningful manner. More specifically, alkyl glycosides carry no charge but still have rigid carbohydrate headgroups. It is therefore important to know the behavior of such systems. The two molecules that we study have polar groups that are very different chemically and structurally. The hexaethylene glycol group can be viewed as a short polymer chain and is more flexible than the rather stiff, disklike maltoside headgroup.5 Because both amphiphiles have the same hydrophobic group, it is the headgroup properties that are responsible for differences in the structure of the micelles that they form. C12E6 has been reported to form cylinders,6 wormlike micelles,7,8 and coexisting spheres and short rods,9 with the latter also predicted by some theoretical calculations.10 These studies also showed that the micelles grow upon increasing temperature or surfactant concentration. In contrast, C12G2 forms globular (4) Garcıa, M. T.; Ribosa, I.; Campos, E.; Sanchez Leal, J. Chemosphere 1997, 35, 545. (5) Persson, C. M.; Kjellin, U. R. M.; Eriksson, J. C. Langmuir 2003, 19, 8152. (6) Cebula, D. J.; Ottewill, R. H. Colloid Polym. Sci. 1982, 260, 1118. (7) Shirai, S.; Yoshimura, S.; Einaga, Y. Polym. J. 2006, 38, 37. (8) Yoshimura, S.; Shirai, S.; Einaga, Y. J. Phys. Chem. B 2004, 108, 15477. (9) Glatter, O.; Fritz, G.; Lindner, H.; Brunner-Popela, J.; Mittelbach, R.; Strey, R.; Egelhaaf, S. U. Langmuir 2000, 16, 8692. (10) Jodar-Reyes, A. B.; Leermakers, F. A. M. J. Phys. Chem. B 2006, 110, 6300.

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micelles at low concentrations.11-13 Small-angle neutron scattering data have been modeled using oblate14 and prolate15 ellipsoids. Mixtures of the two surfactants could, on the basis of the studies mentioned above, be expected to show a transition from globular to elongated aggregates as the amount of C12E6 is increased. Introducing C12G2 could split elongated micelles into smaller ones by introducing a geometry that more easily forms the end caps of the rodlike micelles. We have investigated surfactant mixtures with several different compositions, as well as the two pure systems, at different total concentrations in D2O. Static light scattering (SLS) and smallangle neutron and X-ray scattering (SANS and SAXS) were employed to provide information on micelle masses, growth laws, and the size and shape of the aggregates formed. To be able to analyze SANS and SAXS data from C12E6 and the mixtures, we developed a form factor for cylindrical core-shell particles with spherical end caps that are swollen relative to the cylinder radius. Kaya16 calculated a form factor for this kind of particle. However, we have simplified the expression to allow polydispersity and other effects to be included without excessive computation times. Our model allows the spherocylinders to coexist with spherical micelles. Micelle systems that exhibit the coexistence of small, globular aggregates with rodlike ones have been experimentally observed in solutions of gemini surfactant by cryo-TEM,17 in mixtures of C12G2 and surfactant NP-10 or phenol by analytical ultracentrifugation,18,19 and for micelles of dodecyldimethylamineoxide by dynamic light scattering.20 It has also been predicted for SDS micelles in salt solution,21 where it is explained by swelling of the end caps of rodlike micelles relative to the cylindrical part as a result of better packing in the less-curved cylindrical environment. Between the end caps and the cylinder there will be a region with negative curvature, where the surfactants have higher free energy than in the other parts of the micelle. As a consequence, very short rods will have a very low probability, which in practice will lead to a gap in the micelle size distribution.

Materials and Methods Surfactant Samples. C12E6 was purchased from Fluka (g98.0%), and C12G2 was purchased from Glycon Biochemicals GmbH (>99.5%). Both surfactants were used as received. Single surfactant stock solutions with a concentration of 0.11 mol/L (∼5 wt %) were prepared with D2O (Aldrich, 99.9%). These were then used to make mixtures with 85, 70, 50, 30, and 15 mol % C12E6. Lower-concentration samples were made by diluting the 0.11 mol/L samples. SLS samples were degassed and filtered using 0.02 μm filters (Anotop 25, Whatman) to remove air bubbles and dust. All concentrations were well above the cmc of the two surfactants, reported by Schlarmann and Stubenrauch.22 The measurements were made at 25 C. Static Light Scattering. SLS experiments were performed on a Brookhaven Instruments BI-200SM goniometer with a BI-9000AT digital autocorrelator. The light source was a verti(11) Focher, B.; Savelli, G.; Torri, G.; Vecchio, G.; McKenzie, D. C.; Nicoli, D. F.; Bunton, C. A. Chem. Phys. Lett. 1989, 158, 491. (12) Aoudia, M.; Zana, R. J. Colloid Interface Sci. 1998, 206, 158. (13) Ericsson, C. A.; Soderman, O.; Ulvenlund, S. Colloid Polym. Sci. 2005, 283, 1313. (14) Dupuy, C.; Auvray, X.; Petipas, C. Langmuir 1997, 13, 3965. (15) Cecutti, C.; Focher, B.; Perly, B.; Zemb, T. Langmuir 1991, 7, 2580. (16) Kaya, H. J. Appl. Crystallogr. 2004, 37, 223. (17) Bernheim-Groswasser, A.; Zana, R.; Talmon, Y. J. Phys. Chem. B 2000, 104, 4005. (18) Zhang, R.; Somasundaran, P. Langmuir 2004, 20, 8552. (19) Lu, S. H.; Somasundaran, P. Langmuir 2007, 23, 9188. (20) Majhi, P. R.; Dubin, P. L.; Feng, X. H.; Guo, X. H.; Leermakers, F. A. M.; Tribet, C. J. Phys. Chem. B 2004, 108, 5980. (21) Eriksson, J. C.; Ljunggren, S. Langmuir 1990, 6, 895. (22) Schlarmann, J.; Stubenrauch, C. Tenside, Surfactants, Deterg. 2003, 40, 190.

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cally polarized argon ion laser (Lexel 95-2) with a wavelength of λ0 = 514.5 nm. Static measurements were made at 22 different angles in the interval of 15 e 2θ e 155, where 2θ is the angle between the incident and scattered radiation. Sixty measurements for each angle were averaged and converted to an absolute scale using toluene as a reference   Is ðqÞ -I0 ðqÞ ns 2 dΣðqÞ=dΩ ¼ ðdΣðqÞ=dΩÞref Iref nref

ð1Þ

where dΣ(q)/dΩ is the absolute scattering intensity, I is the measured intensity, and n is the refractive index. Subscripts s, 0, and ref refer to the sample, solvent, and reference, respectively. q = (4πns/λ)sin θ is the modulus of the scattering vector. The angle interval used corresponds to q = 4.23  10-4-31.7  10-4 A˚-1. The intensities were fitted with the Guinier-type expression dΣðqÞ=dΩ ¼

KSLS cMapp 1 þ 13 Rg, app 2 q2

ð2Þ

Here, c is the mass concentration. The micelle molar mass, Mapp, and radius of gyration, Rg,app, are apparent values rather than actual ones because of the possible influence of concentrationrelated interparticle interference effects. KSLS is the optical constant expressed as KSLS ¼

  4π2 ns 2 dn 2 NA λ0 4 dc

ð3Þ

where NA is Avogadro’s number and dn/dc is the refractive index increment. Small-Angle Neutron Scattering. SANS measurements were performed at the SANS-1 instrument at the GKSS Research Center, Geesthacht, Germany. A wavelength of 8.2 A˚ was employed with a wavelength resolution of 10% (fwhm). Four sample-to-detector distances were used (0.71-9.71 m), covering a q range of 0.0057-0.24 A˚-1. Samples were kept in quartz cuvettes with a path length of 2 or 5 mm. Data were azimuthally averaged, corrected for background and detector efficiency, and converted to absolute scale using the incoherent scattering from H2O.23 Instrumental smearing was included in the fitting procedure using resolution functions.24 Small-Angle X-ray Scattering. SAXS measurements were performed with a Nano-STAR (Bruker AXS) instrument using a :: rotating anode (Cu KR) with cross-coupled Gobel mirrors as a 25 source. Samples were kept in quartz capillaries with an inner diameter of about 1.7 mm. The scattering intensity was acquired with a HiSTAR detector (Bruker AXS), and the q range was 0.01-0.35 A˚-1. Data were azimuthally averaged, background subtracted, and converted to an absolute scale using H2O as a reference. Scattering Contrasts. Refractive index increments were measured using a refractometer operating at 590 nm. Three to eight concentrations of the mixtures in D2O, as well as the solvent, were measured. The results are shown in Table 1. Contrasts for SANS and SAXS were calculated using scattering lengths and partial molecular volumes of the surfactants. The partial molecular volume for C12G2 in D2O was calculated from density data obtained with a DMA 5000 density meter from Anton Paar. Three concentrations (0.5, 1, and 2 wt %) were measured as well as the pure solvent. For C12E6, densities from (23) Lindner, P., Scattering Experiments: Experimental Aspects, Initial Data Reduction and Absolute Calibration. In Neutrons, X-rays and Light: Scattering Methods Applied to Soft Condensed Matter; Lindner, P.; Zemb, T., Eds.; Elsevier: Amsterdam, 2002; p 23. (24) Pedersen, J. S.; Posselt, D.; Mortensen, K. J. Appl. Crystallogr. 1990, 23, 321. (25) Pedersen, J. S. J. Appl. Crystallogr. 2004, 37, 369.

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Table 1. Refractive Index Increments of C12E6, C12G2, and Mixtures in D2Oa sample

dn/dc (mL/g)

C12E6 70% 50% 30% C12G2 a Percentages refer to the molar amount of C12E6.

0.137 ( 0.002 0.141 ( 0.001 0.142 ( 0.0002 0.142 ( 0.001 0.147 ( 0.0006

Table 2. Molecular Volumes of a C12 Chain,27 D2O, C12E6, and C12G2 and the Surfactant Headgroup Volumes molecule

molecular volume (A˚3)

headgroup volume (A˚3)

C12 C12E6 C12G2 D2O

352.4 747.8 702.4 30.13

395.4 350.0

Maccarini and Briganti26 were used, although these samples had H2O as a solvent. The results are given in Table 2. Headgroup volumes were obtained by subtracting the C12 tail volume, given by Vass,27 from the total volume.

Results and Discussion Static Light Scattering. Figure 1 shows the apparent molar masses of C12E6, C12G2, and three mixtures as a function of surfactant concentration. Two different kinds of behavior are observed. For samples containing C12E6, Mapp changes with concentration and has a maximum in the middle of the concentration range studied. This reflects micelle growth that is masked by increasing interference effects above the overlap concentration of the rodlike micelles. However, the C12G2 curve is flat, without any signs of either growth or the presence of an overlap concentration. This indicates that the micelles are globular in this concentration interval. The C12G2 micelles have an average molar mass of 70 000 ( 4200 g/mol. This gives an aggregation number of Nagg=137 ( 8, which corresponds well with previously reported values of 132 ( 1014 and 125 ( 10.12 To obtain the molar masses of the other samples, one has to account for the interference effects that cause the scattering intensity to decrease at higher concentrations as well as the micelle growth.28,29 The increase in molar mass is expressed as a growth law of the form Mw ¼ B1 cR

ð4Þ

where Mw is the actual weight-average molar mass and B1 and R are constants. The interference effects can be described by the static structure factor at q = 0, S(0), and the relationship between Mapp and Mw is given by Mapp ¼ Mw Sð0Þ

ð5Þ

Data were analyzed with a model for polymer-like micelles28 that also has been proven to be applicable to shorter rodlike aggregates.30 In this model, S(0) is expressed as31-33   1 2 lnð1 þ XÞ -1 Sð0Þ ¼ 1 þ 9X -2 þ exp 8 X 8 " #9   < 1 = 1 1 þ 1 - 2 lnð1 þ XÞ ð6Þ :2:565 X ; X

(26) Maccarini, M.; Briganti, G. J. Phys. Chem. A 2000, 104, 11451. :: :: (27) Vass, S.; Torok, T.; Jakli, G.; Berecz, E. J. Phys. Chem. 1989, 93, 6553. (28) Schurtenberger, P.; Cavaco, C. J. Phys. II 1993, 3, 1279. (29) Schurtenberger, P.; Cavaco, C. J. Phys. II 1994, 4, 305. (30) Garamus, V. M.; Pedersen, J. S.; Maeda, H.; Schurtenberger, P. Langmuir 2003, 19, 3656. (31) Cannavacciuolo, L.; Pedersen, J. S.; Schurtenberger, P. Langmuir 2002, 18, 2922. (32) Ohta, T.; Oono, Y. Phys. Lett. A 1982, 89, 460. (33) Pedersen, J. S.; Schurtenberger, P. J. Polym. Sci., Part B: Polym. Phys. 2004, 42, 3081.

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Figure 1. Apparent molar mass of mixed micelles of C12E6 and C12G2 as a function of concentration and composition. (0) 100%, (b) 70%, (4) 50%, and (1) 30% C12E6 and (() C12G2. Solid lines are fits to the data by the model for polymer-like micelles. The dashed line is a guide for the eye.

Here, X = c/c* is the reduced concentration, where c* is the overlap concentration. X is related to the second virial coefficient A2 by X ¼

A2 cMw 9 16

-

ln

Mw Mn

ð7Þ

8

Mn is the number-average molar mass. The second virial coefficient scales with Rg and Mw as A2 ≈ ÆR2gæ3/2/M2w and Rg ≈ Mνw, where ν = 0.588 because the situation for micelles with excluded volume interactions corresponds to good-solvent conditions for polymers. A2 can therefore be expressed as A2 = -2 - 2) R(3ν - 2) = B2B(3ν c . If Mw/ Mn ≈ 2, as is expected for B2M3ν w 1 cylindrical micelles, then eq 7 can be rewritten as X ¼ 2:10B1 3ν -1 B2 c½Rð3ν -1Þ þ1

ð8Þ

Combining eqs 4-6 and 8 gives an expression that is fit to the data in Figure 1. The resulting functions are shown as lines in the same graph and describe the experimental values very well. Fit parameters R, B1, and B2 are given in Table 3, together with c* and Mw for micelles formed in 10 g/L solutions at different mixture compositions. Note that both c* and Mw vary with concentration as a result of the concentration-induced growth, and to allow comparisons, we have chosen to give c* and Mw at 10 g/L. The growth exponent R is in reasonable agreement with the mean-field value of 0.5-0.6.34 For the same concentration, the molar mass increases with the amount of C12E6 in the sample. At the same time, the overlap concentration decreases, meaning that the micelles fill a larger part of the space in the solution. From this, we can conclude that the more C12E6, the more favorable for the system to form elongated micelles. (34) Cates, M. E.; Candau, S. J. J. Phys.: Condens. Matter 1990, 2, 6869.

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Article Table 3. SLS Fit Results for Mixtures of C12E6 and C12G2a

sample

B1 (g1 - R mLR mol-1)

B2 (106 L mol3ν - 1 g-3ν)

C12E6 67000 ( 5900 0.82 ( 0.03 70% 65000 ( 3200 0.72 ( 0.02 50% 47000 ( 2000 0.61 ( 0.006 30% 42000 ( 2500 0.53 ( 0.01 a Percentages refer to the molar amount of C12E6. b c = 10 g/L.

Small-Angle Neutron and X-ray Scattering. SANS and SAXS were performed on the same samples, and scattering curves from five sample compositions are shown in Figures 2 and 3. In the SAXS data, there is a pronounced peak at higher q originating from a core-shell structure in the samples because the surfactant head and tail groups have scattering contrasts with opposite signs for this technique. C12E6 (Figure 3a) is almost contrast matched at low q, and it is therefore not possible to get any overall structural information about the micelles from only SAXS. In SANS, this is not an issue because the contrasts of the tail and headgroup in D2O have the same sign. Increasing the fraction of C12E6 in the mixture gives an increase in the forward scattering of data when normalized by the mass concentration. This means that the micelles get larger, in agreement with light scattering, and this is observed already at 15% C12E6 (not shown). Data displayed in Figures 2 and 3 are not normalized, and this trend is therefore not obvious. This is because an increased amount of C12G2 results in a higher surfactant molar mass and mass concentration, which shifts the experimental data to a higher intensity level, an effect that is not related to micelle growth. The data for pure C12G2 micelles level off at low q and are constant over a large range. This is in agreement with the micelles being relatively small and globular as also suggested by the light scattering. The micelles were first modeled as ellipsoids of revolution with a constant shell thickness for the headgroup. However, the model gave aggregation numbers that were only half of the values determined by light scattering. We considered these deviations to be unacceptable because they cannot be explained by uncertainties on the absolute scale, by concentration, or by contrast factors. In the next attempt, the micelles were modeled as monodisperse core-shell discs with a core radius of R, a thickness of D, and a constant shell thickness of T. The form factor for randomly oriented particles is based on the scattering function for cylinders and is given by35 Pd ðqÞ ¼ Z π 2 2J1 ðqðR þ TÞsin φÞ sinðqðD þ 2TÞcos φ=2Þ ΔFo Vo qðR þ TÞsin φ qðD þ 2TÞcos φ=2 0  2J1 ðqR sin φÞ sinðqD cos φ=2Þ 2 sin φ dφ ð9Þ ðΔFo -ΔFi ÞVi qR sin φ qD cos φ=2 where J1(x) is the first-order Bessel function of the first kind. The total volume and that of the core are Vo = π(R + T )2(D + 2T ) and Vi = πR2D, respectively. To have satisfactory fits, interfaces between core and shell and shell and water had to be smeared by multiplying the shell and core amplitudes by exp(-σ2q2/2) where σi and σo are the widths of the inner and outer interfaces, respectively. SANS and SAXS data were analyzed simultaneously. Data from all six concentrations were described well by the model for oblate shapes without having to introduce a structure (35) Pedersen, J. S. Adv. Colloid Interface Sci. 1997, 70, 171.

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R 0.60 ( 0.05 0.58 ( 0.03 0.66 ( 0.02 0.68 ( 0.03

Mw (g mol-1)b

c* (g L-1)b

267 000 247 000 215 000 201 000

42 49 64 75

Figure 2. SANS and SAXS data (upper and lower curves, respectively) for 0.011 mol/L C12G2. Lines are from a fit with the disk model.

factor. A representative fit example is shown in Figure 2. The results confirm that the micelles do not change in the concentration range studied. The values obtained are R = 24.1 ( 0.4 A˚ and D = 21.8 ( 0.4, which gives a half-thickness of 10.9 A˚. The headgroup thickness is T = 11.7 ( 0.3 A˚. The aggregation number calculated from the core volume is Nagg = 113 ( 4, which is still somewhat lower than earlier reported values and what we found with SLS. Probably the results derived from the SANS and SAXS data are more reliable as a result of the fact that the analysis is based on more extensive information because the modeling also has to reproduce the size and structural information contained in the q dependence of the data. We further note that the light scattering results are influenced by uncertainties in the determination of the refractive index increments. Because this parameter is squared in the optical constant, the masses and aggregation numbers determined by light scattering are very sensitive to its value. For C12E6 and the mixtures, the SANS data are quite different from the data for C12G2 also displaying a significant q dependence at low q. To give an impression of the particle shape for these samples, SANS data for 0.011 mol/L were initially analyzed with the indirect Fourier transformation method36 using the implementation described in ref 37. This approach gives the pair distance distribution function, which is an average histogram of all pair distances of points within the particles in the sample weighted by the scattering density of the points. The function for C12E6 is shown in Figure 4a and is comparable to one for the same surfactant published by Glatter et al.9 The shape of the curve is intermediate between that of a sphere and that of a cylinder. This can be seen by comparing it to theoretical curves for the latter two and a combination of them, shown in Figure 4b, indicating that the solution contains both kinds of (36) Glatter, O. J. Appl. Crystallogr. 1977, 10, 415. (37) Pedersen, J. S.; Hansen, S.; Bauer, R. Eur. Biophys. J. Biophys. Lett. 1994, 22, 379.

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Figure 3. SANS and SAXS data (upper and lower curves, respectively) for (a) 100, (b) 70, (c) 50, and (d) 30% C12E6 at a total concentration of 0.011 mol/L. Lines are from fits with the spherocylinder plus sphere model.

aggregates. Similar results were obtained for the mixed surfactant samples at the same concentration. To account for this when modeling SANS and SAXS data, we have developed a new model for scattering from a mixture of cylinders with swollen end caps (spherocylinders) and spheres. Figure 5 describes the spherocylinder structure. Detailed expressions for the form factor are given in the Appendix. The scattering intensity from samples containing C12E6 can be expressed as dΣðqÞ=dΩ ¼

cNA fcyl cNA ð1 -fcyl Þ Icyl ðqÞ þ Is ðqÞ Ms Mn, cyl

ð10Þ

where fcyl is the mass fraction of surfactants in spherocylindrical micelles, Mn,cyl is the spherocylinder number-average molar mass, and Ms is the sphere molar mass. Is(q) = As(q)2 is the scattering intensity from a sphere (Appendix). The spherocylinder intensity Icyl(q) includes a structure factor calculated using the random phase approximation (RPA) Icyl ðqÞ ¼

ÆPcyl ðqÞæ 1 þ βÆPcyl ðqÞæ=ÆPcyl ðq ¼ 0Þæ

ð11Þ

where ÆPcyl(q)æ is the orientationally averaged spherocylinder form factor. β = (1/S(0)) - 1 is a concentration-dependent parameter obtained from the SLS results. In total, 12 parameters were fitted. Two of these were scale factors for SANS and SAXS to correct for small errors in absolute intensity or concentration, and two were corrections to the backgrounds that were close to zero. Five fit parameters describe the geometry of the micelles: Rc,i, the core radius of the cylindrical part of the spherocylinders; R, a scale factor relating the cylinder inner and outer radii to those of the end 7300 DOI: 10.1021/la900336r

caps/spheres; d, the number-average separation of the end cap centers (spherocylinder length); and σi and σo, the widths of the diffuse interfaces, as in the ellipsoid model. The mass fraction of surfactants in spherocylindrical micelles fcyl was also fitted. The hydration of the headgroups was included through fw, the water fraction in the shell. The model implementation employs molecular constraints in terms of molecular volumes and contrasts obtained as described in the Materials and Methods section and the molar composition of the solutions. Aggregation numbers were calculated from the C12 core volume of the particles, which is expected not to include any water. This also gave the dry volume of the headgroups in the shell, and the total scattering length of the shell. The total shell volume, including water, was calculated using fw, which then gave the contrast for this given shell composition. SANS and SAXS data were also analyzed simultaneously in this case. The model gave good fits to the data, shown in Figure 3. The core radius does not vary much, which is expected because the hydrophobic part is the same in all samples. On average, the cylinder core radius Rc,i = 13.7 ( 0.55 A˚. The maximum length of a hydrocarbon chain with nc carbon atoms is given by lmax = 1.5 + 1.265nc,38 which for our surfactants is 16.68 A˚. We can conclude that the hydrophobic groups are not extended in the cylindrical part. Spherical micelles and end caps have a core radius of Rs,i = RRc,i. The model is not very sensitive to changes in R, and for the 0.044 mol/L samples, it was therefore kept constant at 1.32, the average value from the two lower concentrations. If one assumes total conservation of surfactant tail volume and optimal headgroup area when going from the (38) Tanford, C., The Hydrophobic Effect: Formation of Micelles and Biological Membranes, 2nd ed.; John Wiley & Sons: New York, 1980.

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Figure 5. Spherocylinder with end caps swelled relative to the cylinder radius. Coexisting spherical micelles have the same radius as the end caps. The lower picture shows a core-shell model of the same shape.

Figure 4. (a) Pair distance distribution function of 0.011 mol/L C12E6. (b) Pair distance distribution functions of a cylinder (-), a sphere ( 3 3 3 ), and a mixture of the two aggregate types ( 3 - 3 ) with the same total volume in the spheres and in the cylinders.

spherical to the cylindrical geometry, then R should equal 1.5. However, lower values of R are likely because this results in lessnegative curvature between the cylinder and end cap. With our R, one obtains Rs,i = 18.1 A˚. fw varies a lot and is too small because the E6 headgroup is reported to be more hydrated than the maltoside.39 However, in the fits this parameter is strongly coupled to the width of the interface between the shell and water, σo, which describes the gradual penetration of water into the headgroup region and therefore also is related to the hydration of the headgroups. The width grows when fw decreases, and this means that the value of fw should not be taken literally. The width of the interface between core and shell, σi, has an average value of 2.5 ( 0.9 A˚, which is approximately the projected length of two methylene groups and therefore is a reasonable value if the diffuse interface originates from the protrusion of surfactant molecules as they move perpendicular to the interface. The scale factor that had to be applied for the model to agree with the SANS data is 1.00 ( 0.05, whereas the corresponding scale factors for SAXS is in the range of 1.00 ( 0.25. For SAXS, the agreement is very sensitive to the correct estimations of partial volumes of the head and tail of the surfactants because the contrasts are calculated as small differences between similar numbers and furthermore there are “cancelations” in the model of positive and negative contributions that have to be correct. In contrast to this, the neutron contrasts are between hydrogenated and deuterated molecules; therefore, small errors contribute less. This is the explanation for the larger variation in scale factors for SAXS than for SANS. (39) Claesson, P. M.; Kjellin, M.; Rojas, O. J.; Stubenrauch, C. Phys. Chem. Chem. Phys. 2006, 8, 5501.

Langmuir 2009, 25(13), 7296–7303

Weight-average molecular weights can also be calculated from the fit results for the SANS and SAXS data and compared to those obtained with light scattering. In general, the values for SANS and SAXS are systematically lower by about 30%. The main contribution to the discrepancy probably originates from the assumptions invoked in the analysis of the light scattering data. In the analysis, it is assumed that the micelles are cylindrical and therefore that they follow an exponential growth law and that the interference effects can be described by polymer theory. However, the presence of a significant fraction of spherical micelles means that the assumptions are not fully valid, which might lead to systematic errors in the result. We note again that the analysis of the SANS and SAXS data relies on the analysis of the full q dependence, whereas light scattering deals only with the intensity level at low q. We also note again that there are some uncertainties in the determination of the refractive index increments. For the SANS and SAXS results, two parameters change systematically with surfactant concentration and composition: fcyl and d. Figure 6 shows that fcyl increases with surfactant concentration and the amount of C12E6 but that there are still spherical aggregates in all pure C12E6 samples. However, there is a significant number of surfactants in spherocylindrical aggregates when the composition is as low as 15% C12E6. Figure 7 shows the calculated weight-average length of the spherocylindrical micelles. They grow in length with both C12E6 fraction and total concentration. This is in agreement with SLS results and is expected for elongated micelles. Considering that pure C12G2 forms small oblate micelles that do not grow with concentration and that a substantial amount of the surfactants are in spherocylindrical aggregates in the mixtures with the smallest amount of C12E6, the properties of the mixed micelles are dominated by C12E6. For pure C12E6, one observes the coexistence of cylindrical and spherical micelles, and for pure C12G2, one observes only globular micelles. Therefore, it is natural to assume that C12G2 prefers a curved interface whereas C12E6 can have an energetically favorable environment in cylindrical micelles that are less curved. One could therefore suspect that there could be demixing of the surfactant types in the micelles, with C12E6 forming cylindrical parts of the spherocylinders and C12G2 forming end caps and globular micelles. Some information about this can be obtained considering the low overall contrast of C12E6. In the data for mixtures rich in C12G2, there is in the log-log plots a finite slope at low q that is not present in the pure C12G2 data. This slope originates from the presence of elongated aggregates. If the cylindrical part contains mostly C12E6, then it would not be DOI: 10.1021/la900336r

7301

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B€ averb€ ack et al.

Figure 6. Fraction of surfactant mass in spherocylindrical micelles as a function of the amount of C12E6 and concentration: () 0.011 mol/L, (b) 0.022 mol/L, and (2) 0.044 mol/L.

Figure 7. Weight-average lengths of the spherocylindrical micelles as a function of the amount of C12E6 and concentration: () 0.011 mol/L, (b) 0.022 mol/L, and (2) 0.044 mol/L.

observed with SAXS, and the data would look more like those for the pure maltoside. This means that there is not a significant segregation of the surfactants into different aggregate parts/types. The structures of the headgroups of C12E6 and C12G2 are quite different, with a flexible headgroup for C12E6 and a bulky, stiff headgroup for C12G2. When mixing the two, the important point is how the two headgroups pack with one another, rather than how they pack in the pure systems. Because the C12E6 headgroup is flexible and polymer-like with the inclusion of free space for water, it can also easily accommodate the bulky headgroups of C12G2. Therefore, the less curved structures with cylindrical parts are energetically feasible, and the properties of the mixed systems are similar to those of pure C12E6. Although this is a reasonable and logical explanation of how there are synergistic effects in mixtures of nonionic surfactants, it would not have been easy to suggest without detailed experimental investigations such as those carried out in the present work.

Summary and Conclusions We have performed a detailed scattering study of the structural properties of the micelles formed by C12G2 and C12E6 and their mixtures. Light scattering was used to investigate the overall behavior of the systems. The data showed that the micelles of pure C12G2 are globular and do not grow with increasing concentration, whereas the data for C12E6 and the mixtures showed the presence of elongated micelles that grow with increasing concentration. At high concentration, there was a clear influence of interparticle 7302 DOI: 10.1021/la900336r

interference effects. The full concentration dependence could be modeled by employing an exponential growth law and an expression from polymer theory to describe the interference effects. Detailed structural information for the systems was obtained by an analysis of the SANS and SAXS data that display a strong q dependence as a result of the presence of the micelle structures. The very different contrast conditions for SANS and SAXS mean that both the overall shape and the distribution of the components of the core-shell structure can be determined. Modeling revealed that the mixtures and pure C12E6 contain cylindrical and spherical micelles, and this was included in the model of the micelles, which also took into account polydispersity and concentration effects. The number of free parameters of the model was reduced using molecular constraints. By simultaneous analysis of SANS and SAXS data, we have obtained detailed structural information on the micelles and have established that for C12E6 and the mixtures there is a large fraction of the surfactant in spherocylindrical micelles and that the fraction increases with increasing amounts of C12E6. We have also shown that the micelle length grows with increasing fraction of C12E6 in the mixture, as well as with the overall surfactant concentration. These observations lead to the conclusion that the overall behavior of the mixtures is dominated by C12E6 and that the flexible headgroup of this surfactant makes it possible to accommodate the bulkier headgroup of C12G2 without the introduction of large curvature of the micelle surface. There is still the influence of C12G2 on the overall length of the micelles because the micelles are observed to be shorter when more C12G2 is present. In the initial analysis of the light scattering data, the use of a model with a power-law growth law and an expression from polymer theory for describing the interference effects gave good fits to the data and an apparently consistent analysis. This was possible even though the additional presence of the spherical micelles, detected in the further analysis of the SANS and SAXS data, was ignored. However, even if the quantitative results of the analysis of the light scattering data cannot be taken too literally, the presence of concentration-induced micelle growth and interparticle interference effects are clearly demonstrated. Such effects must of course also be present in systems where cylindrical micelles coexist with spherical ones and were also confirmed by the average length of the spherocylindrical micelles as obtained by the analysis of the SANS and SAXS data. The sensitivity of light scattering as to whether the micelles display concentrationinduced growth is also confirmed by a comparison to the behavior of C12G2, for which the light scattering results are markedly different from those of C12E6 and the mixtures and demonstrate that the surfactant forms globular micelles that do not grow with increasing concentration. Acknowledgment. Part of this work was funded by the European Community’s Marie Curie research Training Network “Self-Organisation Under Confinement (SOCON)” (contract no. MRTN-CT-2004-512331). SANS measurements were supported by the European Commission under the sixth Framework Programme through the Key Action “Strengthening the European Research Area, Research Infrastructures” (contract no. RII3-CT-2003-505925). We thank M. Maccarini and G. Briganti for sharing their raw density data with us.

Appendix: Spherocylinder Plus Sphere Model for the Analysis of SANS and SAXS Data We describe the form factor for cylindrical core-shell particles with spherical end caps that are swollen relative to the cylinder Langmuir 2009, 25(13), 7296–7303

B€ averb€ ack et al.

Article

where ΔF is the scattering constrast, Vc is the cylinder volume, and J1(x) is the first-order Bessel function of the first kind. φ is the angle between q and the cylinder axis. The sphere form factor is given by " Ps ðqÞ ¼ ΔF Vs 2

2

3ðsin qRRc -qRRc cos qRRc Þ

#2

ðqRRc Þ3



ΔF2 Vs 2 As ðq, RRc Þ2 ð15Þ where Vs is the sphere volume. The cross terms are Z

π 2

Sc, s ðqÞ ¼ ΔF Vc Vs As ðq, RRc Þ 2

Figure 8. Closer look at the end cap of the spherocylinder.

radius. The full analytical expression for spherocylinders has been calculated by Kaya.16 However, this expression is numerically quite involved, and we have therefore simplified it to allow polydispersity and other effects to be included without excessive computation time. Figure 5 describes the geometry of the spherocylinder in our model. It is built from a cylinder that overlaps slightly with two spheres that form the end caps. The cylindrical part has a radius of Rc and a length of L, and the spheres have a radius of Rs = RRc. Sphere centers are separated by a distance d. A core-shell version is used for micelles, with the inner part described by its own set of Rc and L values but with R and d being the same as for the whole particle. Spheres that coexist with the spherocylinders are core-shell particles of the same size as the end caps. A closer look at the end cap is shown in Figure 8. The overlap region is indicated in black, and its volume is set to be equal to the missing parts of the spherocylinder, colored in gray. In this way, the volume of the model is the same as that of the ideal spherocylindrical model because the extra part on the overlap matches the missing part on the borders. The length d depends on this overlap, quantified by y as a function of R and Rc. It can be shown that for the following expression for y the two volumes are identical: pffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffi R y ¼ ðR - R2 -1Þ2 ð2R þ R -1Þ þ R2 -1 3

Ac ðq, Rc , L, φÞ

0

cosðqd cos φ=2Þsin φ dφ ð16Þ and Ss, s ðqÞ ¼ ΔF2 Vs 2 As ðq, RRc Þ2

sin qd qd

ð17Þ

Combining eqs 13-17 and rewriting the expression gives Z

π 2

Pcyl ðqÞ ¼ ΔF2

½Vc Ac ðq, Rc , L, φÞ þ

0

2Vs As ðq, RRc Þcosðqdcos φ=2Þ2 sin φ dφ ð18Þ The amplitude for the spherocylinder is thus Acyl ðqÞ ¼ Vc Ac ðq, Rc , L, φÞ þ 2Vs As ðq, RRc Þcosðqd cos φ=2Þ ð19Þ This can be used in a core-shell form of eq 18, which is written as Z

π 2

Pcyl, cs ðqÞ ¼ 0

½ΔFo Acyl ðq, Rc, o , Lo , R, d, φÞ -

ð12Þ

ðΔFo -ΔFi ÞAcyl ðq, Rc, i , Li , R, d, φÞ2 sin φ dφ ð20Þ

In the following text, we use general expressions for interference terms for particles with several components.35 The spherocylinder form factor, Pcyl(q), can be written as

Subscripts o and i refer to the outer (shell) and inner (core) parameters, respectively. The spherocylinders are polydisperse in d, which is described by a normalized Shultz-Zimm distribution.

Pcyl ðqÞ ¼ Pc ðqÞ þ 2Ps ðqÞ þ 4Sc, s ðqÞ þ 2Ss, s ðqÞ

ð13Þ

Pc(q) and Ps(q) are the form factors of a cylinder and of a sphere, and Sc,s(q) and Ss,s(q) are cross terms between the two geometries. The cylinder form factor is Pc ðqÞ ¼ ΔF Vc 2

Z π 2

2 0

 2J1 ðqRc sin φÞ sinðqL cos φ=2Þ 2 sin φ dφ qRc sin φ qL cos φ=2 Z π 2  ΔF2 Vc 2 Ac ðq, Rc , L, φÞ2 sin φ dφ ð14Þ

 DðdÞ ¼

   z þ 1 z þ1 dz d exp -ðz þ 1Þ Ædæn Ædæn Γðz þ 1Þ

ð21Þ

Here Ædæn is the number-average length and (z + 1) = Æd æ2n/σ2, with the standard deviation σ. For the expected exponential size distribution, σ is equal to Ædæn. Very short spherocylinders will have a low probability because of the negative curvatures close to the end caps; therefore, we set a lower limit of d and choose it to equal twice the outer radius of the spheres because this is the shortest possible spherocylinder constructed with two spheres as end caps.

0

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DOI: 10.1021/la900336r

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